StudyDataandVisualizations Annex TheImpactofVisualizingUncertaintyonTrainTripSelection

The Impact of Visualizing Uncertainty on Train Trip Selection

Annex

M. Wunderlich, K. Ballweg, and T. von Landesberger

Part I

Study Data and Visualizations

1 Description of the Train Trips

Attribute TO1 TO2 TO3

Departure ≈ b≺a a ≺S b

Arrival a ≺S b, b≺D a b≺a b≺S a, a≺D b

Travel duration a ≺S b, b≺D a b≺a a ≺S b, ≈D

Transfers no transfers 2 in a and b, longer in a 1 in b Delays a’s delay meets deadline (C2) never critical critical transfer

Alternatives none none 1 for b’s transfer

Table 1: Attribute-wise comparison of the two train trips TO1–TO5 per decision situation. (a denotes the first, b the second trip;≈similar for a and b; shorter/earlier with a: a≺b; according to schedule: S; according to (maximum) expected delays: D)

Attribute TO4 TO5

Departure a ≺b ≈

Arrival ≈ a ≺S b, b≺D a

Travel duration b ≺a ≈S, b ≺Da Transfers 2 in b 1 in a and b

Delays never critical critical transfers Alternatives none 1 for each transfer

Table 2: Attribute-wise comparison of the two train trips TO1–TO5 per decision situation. (a denotes the first, b the second trip;≈similar for a and b; shorter/earlier with a: a≺b; according to schedule: S; according to (maximum) expected delays: D)

TO1 Direct influence of train delay on the arrival time: Both train trips depart at the same time and have no transfers. The travel duration with the first connection is shorter according to the schedule while the travel time with the second connection is shorter according to the (maximum) expected delays.

TO2 Influence of delay on transfer time: Departure and arrival times of the two trips are similar whereas the travel duration with the second trip is slightly shorter. Each trip has two transfers.

The transfer durations of the first connection are longer according to the schedule but shorter

TO3 Influence of a critical delay on arrival time via potential miss of a connecting train: The travel duration of the first trip is longer but the trip contains no transfers. The second trip contains one transfer that is also critical, i.e., the connecting train of the second connection might be missed due to the expected delays. If the connecting train is missed, the arrival time of the second trip is before the arrival time of the first trip. If the connecting train is reached, the order of the arrival times is vice versa.

TO4 Trade off between travel duration and transfers: The arrival time of both trips is similar. The first trip contains no transfers but departs earlier, i.e., its travel duration is longer. The second trip contains two transfers but none of them is critical (i.e., the connecting trains will most probably will be reached).

TO5 Influence of arrival time due to critical delay: Each of the trips contains one transfer of equal duration. The connecting trains in both trips might be missed due to the delay of the preceding trains. The arrival time of the first connection is earlier if the connecting train is reached and later otherwise.

2 Visulizations of the Train Trips

Figure 1: Train Trips TO1 displayed with designD_cum

Figure 3: Train Trips TO3 displayed with designDcum

Figure 4: Train Trips TO4 displayed with designD_cum

Figure 5: Train Trips TO5 displayed with designDcum

Figure 6: Train Trips TO1 displayed with design Dnoncum

Figure 7: Train Trips TO2 displayed with design Dnoncum

Figure 8: Train Trips TO3 displayed with design Dnoncum

Figure 9: Train Trips TO4 displayed with design Dnoncum

Figure 10: Train Trips TO5 displayed with designDnoncum

Figure 11: Train Trips TO1 displayed with designDvis

Figure 12: Train Trips TO2 displayed with designDvis

Figure 13: Train Trips TO3 displayed with designD_vis

Figure 14: Train Trips TO4 displayed with designDvis

Figure 15: Train Trips TO5 displayed with designD_vis

Figure 16: Train Trips TO1 displayed with designDtext

Figure 17: Train Trips TO2 displayed with designD_text

Figure 18: Train Trips TO3 displayed with designDtext

Figure 19: Train Trips TO4 displayed with designDtext

Figure 20: Train Trips TO5 displayed with designDtext

Part II

Study Results

3 Decisions

T1

!"#$"

!_%&' !()(%&' !_*+,

(c) Train connections TO1 and temporal constraint C1

T1

!"#$"

!%&' !()(%&' !*+,

(d) Train connections TO1 and temporal constraint C2

T2

!"#$"

!%&' !()(%&' !*+,

(g) Train connections TO2 and temporal constraint C1

T2

!"#$"

!_%&' !()(%&' !_*+,

(h) Train connections TO2 and temporal constraint C2

T3

T3

T4

!"#$"

!%&' !()(%&' !*+,

(c) Train connections TO4 and temporal constraint C1

T4

!"#$"

!_%&' !()(%&' !_*+,

(d) Train connections TO4 and temporal constraint C2

T5

!"#$"

!%&' !()(%&' !*+,

(g) Train connections TO5 and temporal constraint C1

T5

!"#$"

!%&' !()(%&' !*+,

(h) Train connections TO5 and temporal constraint C2

Figure 22: Distribution of the decisions for each situation composed of a set of train connections TO1–TO5 and a temporal constraint C1/C2. The values are relative to the number of answers for each design. Option 1, Option 2, For me, both trips are of equal value, I can not decide based on this depiction, because: [text input], andI don’t know

4 Statistical Evaluation

4.1 Dependence on the Availability of Delay Uncertainty

TheFisher’s Exact Test showed that the decisions on train trip selection significantly depend on the availability of delay uncertainty visualization for eight out of ten decision scenarios (cf. Table 3).

C1 C2

TO1 <0.001 *** <0.001 ***

TO2 <0.001 *** <0.001 ***

TO3 <0.001 *** <0.001 ***

TO4 1 0.281

TO5 <0.001 *** <0.001 ***

Significance levels: p-value<0.001: ***,<0.01: **,<0.05: *

Table 3: P-values according to Fisher’s Exact Test for decisions depending on the availability of delay uncertainty information in the visualization.

4.2 Dependence on the Design of Connection Display

We tested whether decisions differ depending on the type of display with Fisher’s Exact Test. We specifically analyzed two cases: with uncertainty (Dcum and Dnoncum) and without uncertainty (Dvis andDtext).

C1 C2

TO1 <0.001 *** <0.001 ***

TO2 <0.001 *** <0.001 ***

TO3 0.001 ** <0.001 ***

TO4 0.047 * 0.336

TO5 <0.001 *** <0.001 ***

Significance levels: p-value<0.001: ***,<0.01: **,<0.05: *

Table 4: P-values according to Fisher’s Exact Test for decisions depending on the design of train trip display.

Dcum vs. Dnoncum Dvis vs. Dtext

TO1 C1

0.002 **^◦ 0.752

TO2 0.74 0.396

TO3 1 0.116

TO4 0.023 * 0.106

TO5 0.332 0.04 *

TO1 C2

1 1

TO2 1 0.115

TO3 0.593 0.729

TO5 0.839 0.32

Significance levels: p-value<0.001: ***,<0.01: **, ¡ 0.05: * Bonferroni corrected: p-value<0.0002: ^◦◦◦,<0.002: ^◦◦,<0.008: ^◦

Table 5: P-values according toPost-hoc Fisher’s Exact Test for decisions depending on the type of delay display and depending on whether display is visual or text.

4.3 Dependence on the Existence of an Arrival Deadline

TO1 TO2 TO3 TO4 TO5

† <0.001 *** ^† 0.096 0.029 * 0.789 ^† 0.08

† includes the decision that both connections are of equal value Significance levels: p-value<0.001: ***,<0.01: **,<0.05: *

Table 6: P-values according toMcNemar Test for decisions depending on the time constraint.

Dcum &Dnoncum Dvis&Dtext

TO1 0.004 **

TO2 1 ^† 0.039 *

TO3 1 0.034 *

TO4 0.221 0.724

TO5 1 ^† 0.096

† includes the decision that both connections are of equal value Significance levels: p-value<0.001: ***,<0.01: **,<0.05: *

Table 7: P-values according to McNemar Test for decisions depending on the time constraint for designs with uncertainty (Dcum & Dnoncum) and without uncertainty (Dvis & Dtext).

D_cum D_noncum D_vis D_text TO1 0.023 * 0.248

TO2 1 ^† 0.059 0.48

TO3 1 0.505 0.046 *

TO4 1 0.248 0.134 0.617

TO5 1 0.48 1

† includes the decision that both connections are of equal value Significance levels: p-value<0.001: ***,<0.01: **,<0.05: *

Table 8: P-values according to McNemar Test for decisions depending on the time constraint for each design.

5 Decision Making Durations

Table 9: Decision Making Durations

D4 D1 D2 D3

2060100140

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D4 D1 D2 D3

10305070

T1C1

T1C2

!"#$" !%&' !()(%&' !*+,

(a) TO1 C1

D4 D1 D2 D3

2060100140

!"#$" !%&' !()(%&' !*+,

D4 D1 D2 D3

10305070

T1C1

T1C2

!"#$" !%&' !()(%&' !*+,

(b) TO1 C2

D4 D1 D2 D3

050100150

D4 D1 D2 D3

20406080

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

T2C1

T2C2

(c) TO2 C1

D4 D1 D2 D3

050100150

D4 D1 D2 D3

20406080

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

T2C1

T2C2

(d) TO2 C2

D4 D1 D2 D3

020406080120

D4 D1 D2 D3

20406080120

T3C1

T3C2

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

(e) TO3 C1

D4 D1 D2 D3

020406080120

D4 D1 D2 D3

20406080120

T3C1

T3C2

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

(f) TO3 C2

D4 D1 D2 D3

050100150

D4 D1 D2 D3

02060100140

T4C1

T4C2

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

(g) TO4 C1

D4 D1 D2 D3

050100150

D4 D1 D2 D3

02060100140

T4C1

T4C2

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

(h) TO4 C2

D4 D1 D2 D3

20406080

D4 D1 D2 D3

050100150

T5C1

T5C2

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

(i) TO5 C1

D4 D1 D2 D3

20406080

D4 D1 D2 D3

050100150

T5C1

T5C2

!"#$" !%&' !()(%&' !*+,

!"#$" !%&' !()(%&' !*+,

(j) TO5 C2

Figure 23: Decision Making Durations